[Footnote:  The diagram which, in the original, is placed above line 2, is similar to the one, here given on page 73 (section 120).—­The diagram here given in the margin stands, in the original, between lines 3 and 4.]

221.

A body illuminated by the solar rays passing between the thick branches of trees will produce as many shadows as there are branches between the sun and itself.

Where the shadow-rays from an opaque pyramidal body are intercepted they will cast a shadow of bifurcate outline and various depth at the points.  A light which is broader than the apex but narrower than the base of an opaque pyramidal body placed in front of it, will cause that pyramid to cast a shadow of bifurcate form and various degrees of depth.

If an opaque body, smaller than the light, casts two shadows and if it is the same size or larger, casts but one, it follows that a pyramidal body, of which part is smaller, part equal to, and part larger than, the luminous body, will cast a bifurcate shadow.

[Footnote:  Between lines 2 and 3 there are in the original two large diagrams.]

IV.

Perspective of Disappearance.

The theory of the “Prospettiva de’ perdimenti” would, in many important details, be quite unintelligible if it had not been led up by the principles of light and shade on which it is based.  The word “Prospettiva” in the language of the time included the principles of optics; what Leonardo understood by “Perdimenti” will be clearly seen in the early chapters, Nos. 222—­224. It is in the very nature of the case that the farther explanations given in the subsequent chapters must be limited to general rules.  The sections given as 227—­231 "On indistinctness at short distances” have, it is true, only an indirect bearing on the subject; but on the other hand, the following chapters, 232—­234, "On indistinctness at great distances,” go fully into the matter, and in chapters 235—­239, which treat “Of the importance of light and shade in the Perspective of Disappearance”, the practical issues are distinctly insisted on in their relation to the theory.  This is naturally followed by the statements as to “the effect of light or dark backgrounds on the apparent size of bodies" (Nos. 240—­250). At the end I have placed, in the order of the original, those sections from the MS. C which treat of the “Perspective of Disappearance” and serve to some extent to complete the treatment of the subject (251—­262).

Definition (222. 223).

222.

OF THE DIMINISHED DISTINCTNESS OF THE OUTLINES OF OPAQUE BODIES.

If the real outlines of opaque bodies are indistinguishable at even a very short distance, they will be more so at long distances; and, since it is by its outlines that we are able to know the real form of any opaque body, when by its remoteness we fail to discern it as a whole, much more must we fail to discern its parts and outlines.